Prediction of Future Failures for Heterogeneous Reliability Field Data

Abstract

This article introduces methods for constructing prediction bounds or intervals for the number of future failures from heterogeneous reliability field data. We focus on within-sample prediction where early data from a failure-time process is used to predict future failures from the same process. Early data from high-reliability products, however, often have limited information due to some combination of small sample sizes, censoring, and truncation. In such cases, we use a Bayesian hierarchical model to model jointly multiple lifetime distributions arising from different subpopulations of similar products. By borrowing information across subpopulations, our method enables stable estimation and the computation of corresponding prediction intervals, even in cases where there are few observed failures. Three applications are provided to illustrate this methodology, and a simulation study is used to validate the coverage performance of the prediction intervals.

Keywords:

• Bayesian estimation
• Censored data
• Dynamic data
• Prior information
• Reliability prediction
• Warranty returns

Supplementary Materials

Supplementary file:

All figures for the Backblaze predictions. A sensitivity analysis of the prior distributions for the Backblaze application. All predictions for the Product A application. The complete set of simulation results. A subset of trace plots for all three applications. A list of the drive-model brand names for the Backblaze application. (pdf)

Data and Code:

Data for all three applications. Both R and Stan code to run the models for all three applications and generate predictions. (zip file)